Results of check:
A_sub can first
A_sub::first
A_sub cannot do SUPER::first
A_sub can second
A::second
A_sub cannot do SUPER::second

Results of check_sub:
A_sub can first
A_sub::first
A_sub can SUPER::first
A::first
A_sub can second
A::second
A_sub can SUPER::second
A::second